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Theorem lem3.3.3lem2 1050
Description: Lemma for lem3.3.3 1052.
Assertion
Ref Expression
lem3.3.3lem2 (a ==5 b) =< (b ->1 a)
Proof of Theorem lem3.3.3lem2
StepHypRef Expression
1 lear 161 . . . 4 (a' ^ b') =< b'
21leror 152 . . 3 ((a' ^ b') v (a ^ b)) =< (b' v (a ^ b))
3 ax-a2 31 . . 3 ((a ^ b) v (a' ^ b')) = ((a' ^ b') v (a ^ b))
4 ancom 74 . . . 4 (b ^ a) = (a ^ b)
54lor 70 . . 3 (b' v (b ^ a)) = (b' v (a ^ b))
62, 3, 5le3tr1 140 . 2 ((a ^ b) v (a' ^ b')) =< (b' v (b ^ a))
7 df-id5 1047 . 2 (a ==5 b) = ((a ^ b) v (a' ^ b'))
8 df-i1 44 . 2 (b ->1 a) = (b' v (b ^ a))
96, 7, 8le3tr1 140 1 (a ==5 b) =< (b ->1 a)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ==5 wid5 22
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-id5 1047
This theorem is referenced by:  lem3.3.3lem3  1051
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